SOLUTION: A thee hour river cruise goes 15km upstream and then back again. The river has a current of 2km an hour. What is the boat's speed and how long was the upstream journey?

Question 807766: A thee hour river cruise goes 15km upstream and then back again. The river has a current of 2km an hour. What is the boat's speed and how long was the upstream journey?
Answer by josgarithmetic(39616) (Show Source): You can put this solution on YOUR website!
r = boat speed if no current present.
c = 2 km/h current of river.
u = time going upstream
3-u = time going downstream (based on description and on assignment of u)

________________speed____________time___________distance(km)
Upstream________r-c______________(u)__________(___)
Downstream______r+c______________(3-u)__________(___)
Total______________________________3_____________15

Two unknown variables , r and u. Filling in the distance data,
________________speed____________time___________distance(km)
Upstream________r-c______________(u)__________((r-c)(u))
Downstream______r+c______________(3-u)__________((r+c)(3-u))
Total______________________________3_____________15

The "Total" data gives an equation:

'
Steps

Substituting for c=2,

This is still one equation in TWO unknown variables.

This will have infinite solutions but there is a restriction.
is that restriction. You may compute r accordingly for its RANGE.

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